Shape Optimization - an introduction

Research Horizons Seminar
Wednesday, January 28, 2009 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 255
Antoine Henrot – University of Nancy, France
Craig Sloane
In this talk, we give an insight into the mathematical topic of shape optimization. First, we give several examples of problems, some of them are purely academic and some have an industrial origin. Then, we look at the different mathematical questions arising in shape optimization. To prove the existence of a solution, we need some topology on the set of domains, together with good compactness and continuity properties. Studying the regularity and the geometric properties of a minimizer requires tools from classical analysis, like symmetrization. To be able to define the optimality conditions, we introduce the notion of derivative with respect to the domain. At last, we give some ideas of the different numerical methods used to compute a possible solution.